2< 4x - 10 < 6

a: -3 < x < -1

b: 2 < x < 4

c: 4 < x < 12

d: -16 < x < -8

and explain how to get to the answer

  B:  2 < x < 4

Step-by-step explanation:

Add 10 to the equation. This gives ...

  8 < 4x < 16

Now, divide the equation by 4.

  2 < x < 4 . . . . . matches choice B

The first step is always "look at what you are given." The second step is always, "determine what you are being asked for."

Here, you're given a compound inequality with the variable multiplied by something and something else added  to that product. To solve for the variable, you must "undo" the addition, then "undo" the multiplication.

Of course, the inverse operation for addition is adding the opposite, or subtraction (however is easiest for you to think about it). Since -10 is added, adding the opposite means adding +10.

The rules of equality (and of "inequality") require that all parts of the equation get the same treatment. We must add 10 to the left side, the middle, and the right side in order for the relationships to remain valid.

Doing that gives ...

  -2+10 < 4x -10 +10 < 6+10

Simplifying that gives the inequality shown above:

  8 < 4x < 16

Now we have an inequality in which x is multiplied by 4. To "undo" that, we multiply by the inverse of 4, that is, we multiply by 1/4. Of course, this is exactly the same as dividing by 4. Again, we have to do this to all three parts of the relation.

This multiplier is a positive number, so we don't need to make any adjustments to the relationship symbols when we do the multiplication. We get ...

  8(1/4) < 4(1/4)x < 16(1/4)

Simplifying gives the

  2 < x < 4

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Side comment (not applicable to this problem)

Had the x-coefficient been negative, our "undo" operation would have been multiplication (or division) by a negative number. When doing that, the direction of the relationship symbols must be reversed. Consider, for example, 2 > 1. Multiplying this by -1 gives -2 < -1. The > must be changed to < to make the relationship stay true.

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.